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Let vector v=[2,-1,1,3], x=[-1,2,-1,-1], y=[0,0,2,1], z=[1,1,2,3]

Are these vectors linearly independent?

If not, give one nontrivial solution of the corresponding system of linear equation,and write one dependency equation

Questioner: Michelle

Country: Quebec, Canada

Category: Advanced Math

Private: Yes <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< changed.

Subject: Linear algebra

Question: Let vector v=[2,-1,1,3], x=[-1,2,-1,-1], y=[0,0,2,1], z=[1,1,2,3]

Are these vectors linearly independent?

If not, give one nontrivial solution of the corresponding system of linear equations,and write one dependency equation

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No, they are not. If you form their matrix:

[2, -1, 1, 3]

[-1, 2,-1,-1]

[0, 0, 2, 1]

[1, 1, 2, 3]

and do Gauss row-reduction, you get something like this:

[1, 1, 2, 3]

[0, 1, 1, 1]

[0, 0, 2, 1]

[0, 0, 0, 0]

So take the third equation as:

2x3 + x4 = 0

and make x4 the parameter. Solve back for the others.

.....................................

Next time, tell me:

-- what do you know about the example?

-- what do your vocabulary terms mean?

-- what have you tried?

and I won't start to think you are just dumping your homework on us.

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